REVIOUS ANSWERS ASK YOUR TEACHER An airplane is flying in still air with an airspeed of 475 miles per hour The plane is climbing at an angle of \( 32^{\circ} \). Find the rate (in mi/hr) at which the plane is gaining altitude. (Round your answer to four decimal places.) \begin{tabular}{|} \& \( \mathrm{mi} / \mathrm{hr} \)\end{tabular}

To find the rate at which the plane is gaining altitude, we need to calculate the vertical component of the plane's velocity. Given: - Airspeed of the plane = 475 miles per hour - Angle of climb = \(32^{\circ}\) We can use trigonometry to find the vertical component of the plane's velocity. The vertical component of the velocity is given by: \[ \text{Vertical velocity} = \text{Airspeed} \times \sin(\text{Angle of climb}) \] Substitute the given values: \[ \text{Vertical velocity} = 475 \times \sin(32^{\circ}) \] Now, we can calculate the vertical velocity to find the rate at which the plane is gaining altitude. The vertical velocity at which the plane is gaining altitude is approximately 261.927674 miles per hour. Therefore, the rate at which the plane is gaining altitude is approximately 261.927674 miles per hour.